Bismuth voltage multiplier and divider



March 11, 1958 J. L. BOWER 2,326,353

BISMUTH VOLTAGE MULTIPLIER AND DIVIDER Filed Feb. 25. 1952 DIRECT COUPLED AMPLIFIER 4 mmvron.

JOHN L. BOWER ATTORNEY United States Patent BISMUTH VOLTAGE MULTIPLIER AND DIVIDER John L. Bower, Downey, Califi, assig'nor to North American Aviation, Inc.

Application February 25, 1952, Serial No. 273,206

16 Claims. (Cl. 235-61) This invention relates to means for precisely multiplying or dividing one arbitrary voltage function of time by another arbitrary voltage function of time.

It is common in the electrical computing art to require means for instantaneously multiplying or dividing one instantaneous voltage by another instantaneous voltage. These instantaneous voltages must, for many applications, be instantaneous values of voltage functions which are varying rapidly with respect to time. The voltages upon which the operation is to'be performed may originate from voltage sources of high impedance, and the source impedance of each of the voltages may be different.

There are several types of multipliers available, all of which have one or more failings. The input impedance of the device may be low, causing a large amount of current to be drawn from the sources, with resultant drop in voltage applied across the terminals of the device. There may be a time lag in one or more of the circuits with the result that the proper voltages do not combine properly if one of the voltage functions varies rapidly. With a zero voltage input the output of the device may not be zero due to drift in the values of the electrical components.

This invention contemplates a multiplier or divider, or both, in which all of the input impedances are high; in which there is no time lag between the application of the input voltage and the extraction of the output voltage; and in which the output voltage is afiirmatively held at zero when one of the multiplier-voltages is zero. The invention finds particular application as a modulator which is a multiplier of sinusoidal voltages. This invention further contemplates providing a resistance element whose resistance varies as a predetermined function of time.

It is therefore an object of this invention to provide electrical means for precisely multiplying or dividing one arbitrary instantaneous voltage by another arbitrary instantaneous voltage by utilizing the properties of bismuth which cause the resistance of resistors fabricated of bismuth to vary with the strength of a magnetic field surrounding said resistors.

It is another object of this invention to provide a voltage multiplier or divider with high input impedances.

It is another object of this invention to provide a voltage multiplier or divider which will supply an undistorted output voltage. I

It is another object of this invention to provide a voltage multiplier or divider wherein the time delay between the modulating voltage and the voltage after modulation is negligible.

It is a further object of this invention to provide a voltage multiplier or divider wherein the voltage output is zero for a multiplying voltage of zero.

It is another object of this invention to provide a voltage multiplier or a voltage divider wherein two bismuth resistors are placed within an electromagnetic field, the first of said resistors being adapted to control by servo means the magnetic flux density of said electromagnetic ICC field whereby the resistance of the first of said bismuth resistors is controlled in synchronism with an external voltage and the resistance of the second of said bismuth resistors is controlled in synchronism with the resistance of the first of said bismuth resistors.

Other objects of invention will become apparent from the following description taken in connection with the accompanying single figure which is a schematic diagram of the invention.

The figure is divided into three convenient parts: a voltage-comparing servo network 21, a magnet circuit 22, and a response circuit 20. Circuit 21 supplies a voltage to high gain direct coupled amplifier 12 between terminals 13 and 14. Source voltages E and E, supplied between terminal 24 and ground, and terminal 23 and ground, respectively, supply an input voltage to direct coupled amplifier 12 through bismuth resistors 5 and 6 as well as through precision resistors 7, 8, 9, 10 and 11. Resistor 6 in circuit 21 and resistor 4 in circuit 20 are fabricated of bismuth for temperature compensation purposes only. High gain direct coupled amplifier 12 controls the flow of current through coil 16 in circuit 22 by means of vacuum tube 15, thereby controlling the magnetic flux density of magnet 17. Since bismuth resistors 3 and 5 are within the magnetic field of magnet 17, their resistances vary with said magnetic field. Changes in the resistance of resistor 5 result in a varying voltage at the junction between the resistors 5 and 6 with respect to the voltage at the junction between resistors 7 and 8. This voltage is compared to source voltage E; by the network of resistors 5, 6, 7, 8, 9, 10, and 11. The difierence between the voltage supplied to terminals 13 and 14 by voltage source E through resistors 5, 6, 7, 8, 9, 10, and 11, and the voltage supplied to terminals 13 and 14 by source voltage B, through resistors 5, 6, 7, 8, 9, 10, and 11 controls the flow of current in circuit 22 by means of direct coupled amplifier 12 and vacuum tube 15. Thus it may be seen that the combination of resistors 5, 6, 7, 8, 9, 10, and 11 together with direct coupled amplifier 12, vacuum tube 15, coil 16, and magnet 17 forms a closed servo loop for comparing the voltage generated between the junction of resistors 5 and 6 and the junction of resistors 7 and 8 on the one hand, and the source voltage E on the other. If the gain of direct coupled amplifier 12 is very high, the voltage generated between the junction of resistors 5 and 6, and the junction of resistors 7 and 8 will follow source voltage E The voltage fluctuation generated between the junction of resistors 5 and 6 and resistors 7 and 8 due to the change of resistance of resistor 5 must be proportional to source voltage E thus requiring the change in resistance of resistor 5 to increase as source voltage E decreases.

Circuit 20 comprising resistors 1, 2, 3, and 4 of which resistors 3 and 4 are of bismuth, effectively multiplies the source voltage E (supplied between terminals 18 and 19) by source voltage E and divides the result by source voltage E by virtue of the change of resistance of bismuth resistor 3 in synchronism with the change of resistance of bismuth resistor 5 in circuit 21. The changes in resistance of bismuth resistor 3 cause the volttage between terminal 25 and ground-hereafter designated Ef-to vary in direct proportion to E and in inverse proportion to E Because of the Wheatstonc bridge configuration of resistors 1, 2, 3, and 4, E, must also vary directly in proportion to voltage source E The resultant voltage at E must therefore be directly proportional to the product of source voltages E and E divided by source voltage E Basically, it is desired to establish the ratio of output voltage E, to source voltage E equal to the ratio of source voltage E to source voltage 13,. After the desired ratio is established, source voltage E may be set at a direct current voltage, thereby acting as a fixed scale factor for the voltages to be multiplied. If the voltages to be instantaneously multiplied are source voltages E and E the product voltage is E One voltage may be divided by another voltage by making E the dividend voltage, and E the divisor voltage, with a resultant quotient voltage of E Alternatively, one voltage may be divided by another by making E the dividend voltage, and E the divisor voltage, with a resultant quotient voltage of B In operation, the device depends upon the specific properties of bismuth whereby the resistance of a bismuth resistor subjected to a magnetic field varies with said magnetic field.

The voltage between terminal 13 and ground, and terminal 14 and ground may be designated E and E respectively, resulting in a voltage between terminals 13 and 14 of E E In the equations which follow, R designates the value of the resistance, while the number associated with each R designates the resistor. I designates only the variable portion of the current flowing through coil 16.

One of the preliminary requirements of this device is that the resistance of resistor 9 be very much greater than the resistance of the parallel combination of resistors 5 and 6, as outlined in the equation:

Another preliminary requirement of this device is that the voltage-dividing network comprising resistor 11 in series with the parallel combination of resistors 7 and 8 divide voltages in the same ratio as the voltage-dividing network comprising resistors and 9, respectively. The resistance of the parallel combination of resistors 5 and 6 may be neglected. Thus:

Voltage E may be derived by first reducing source voltage E to zero to solve for the voltage contributed to E by source voltage E then reducing source voltage E to zero to solve for the voltage contributed to E by source voltage E then combining the results.

The resistance of resistor 9 is very much greater than the resistance of resistor 6. The voltage due to source voltage E across the terminals of resistor combination 9 and 10 is only that due to the voltage-dividing properties of resistor combination 5 and 6, and therefore equal to This voltage is again divided by resistor combination 9 and 10, giving a net voltage E contributed by voltage E of The voltage E is obtained from source voltage E through a voltage-dividing network comprising resistor 7 This is the voltage supplied to direct-coupled amplifier 12 under quiescent conditions. A changing current in coil 16 due to a change in source voltage E causes the resistance of bismuth resistors 3 and 5 to change.

The ratio of resistances experiences a variation approximately proportional to the variation in current in coil 16. Thus,

R s R5+R. R1+R8 is true for a balanced bridge, where 1" represents only the change from the quiescent value of the current in coil 16. This resistance-current relationship is an expression of the fact that the change in ratio is the same for any bismuth voltage divider of the same original ratio when placed within the field of the magnet 17 and experiencing the same flux change.

Since the resistance values are so chosen that for a predetermined value of current the bridge is in balance for the value of R corresponding to such current, there is a value of current at which Ra Ra Rrl-R. Rz-i-Rs if E, or E changes to cause a voltage unbalance and change in the current in the coil 16, R will change and the ratio Ra o I may be shown to be equal to a function H of the gain of direct coupled amplifier 12 and the input voltage E -E across terminals 13 and 14.

Thus:

By taking the limit of this equation as H becomes increasingly large, an approximation for the change in current I when the gain of direct coupled amplifier 12 the constant K by which the current must be multiplied to obtain the change in the ratio From the voltage-dividing characteristics of the Wheatstone bridge resistors 1, 2, 3, and 4 where the minus sign may be taken care of by reversing the terminals at E if necessary.

By Rg=Rm,

E E2=F;'E1

which is the desired result. A change in the ratio of resistances of 1, 2, 3, and 4 so that & R R R5 By designing the magnet 17 and amplifier 12 to handle the frequencies expected, the impedances looking into the amplifier may be adjusted arbitrarily high to match the source impedances of the source voltages by adjusting the values of the various elements of the networks.

If the gain of amplifier 12 remains high for the expected frequencies, the output voltage at B, does not experience distortion or phase shift with reference to the input voltages.

When the voltage at E is zero, the voltage at E, is zero. When the voltage at E is zero, the voltage at E is held at zero by amplifier 12.

To broadly summarize the invention, bismuth resistor 3 may be used as an electrical element whose resistance is slaved to the resistance of another bismuth resistor 5 by virtue of a common magnetic field for both bismuth resistors, the bismuth resistor 5 being adapted to control the field strength of said magnetic field by servo means in response to a desired signal whereby the resistance of bismuth resistor 3 is forced to follow the desired signal. Controlled resistor 3 may then be used in any external circuit where resistors are customarily used. One of the particular applications is, of course, the multiplier and divider shown in the figure.

Inasmuch as controlled bismuth resistor 3 may be used in any external circuit where resistors are customarily used, additional bismuth resistors (not shown) may also be inserted within the magnetic field of magnet 17 to be controlled thereby. Each of the plurality of additional resistors may also be used in any external circuit where resistors are customarily used. Each additional controlled resistor may, for example, be used in another Wheatstone bridge to multiply a voltage applied at the input of said bridge by the ratio of voltage E to voltage E It is not intended, however, to limit the controlled resistors to use in a Wheatstone bridge.

Although the invention has been described and illustrated in detail, it is to be clearly understood that the same is by way of illustration and example only and is not to be taken by way of limitation, the spirit and scope of this invention being limited only by the terms of the appended claims.

I claim:

1. Means for causing the resistance of a bismuth resistor to vary accurately in response to variation in a function of at least one independent variable voltage comprising a controlled bismuth resistor having the property of varying in resistance with magnetic field, a controlling bismuth resistor having the same property, first and second terminal means for application of first and second independent arbitrary voltages, one of which constitutes a control signal, resistance means forming with said controlling bismuth resistor a resistance network including a junction terminal at which a comparison voltage is adapted to appear, the first of said terminal means being connected to said resistance network for energizing it to produce a comparison voltage at said junction terminal, an electromagnet, servo means connected thereto and having input terminals to which said second terminal means and said network junction terminals are differentially connected for rendering the servo means responsive to relationship of voltages at said second terminal means and the said junction terminal, said bismuth resistors being with in the magnetic field of said electromagnet, said servo means being connected to control the field strength of said electromagnet in response to the deviation from a predetermined relationship between voltages at said second terminal means and said junction terminal so that said de- .viation approaches zero, whereby the resistance of said controlled bismuth resistor is caused to vary in proportion to the resistance of said controlling resistor.

2. A device as recited in claim 1 wherein said controlled bismuth resistor forms a branch of a Wheatstone bridge across which a third arbitrary voltage is placed whereby said third arbitrary voltage is instantaneously multiplied b v the voltage of said control signal, and a voltage proportlonal to the product of said third arbitrary voltage and said control signal appears at the output of said Wheatstone bridge.

3. A device as recited in claim 1 wherein said controlled bismuth resistor forms a branch of a Wheatstone bridge across which a third arbitrary voltage is applied whereby one of said second and third arbitrary voltages is instantaneously divided by the voltage at said first terminal means, and a voltage proportional to the quotient of said division appears at the output of said Wheatstone bridge.

4. A device as recited in claim 1 wherein said controlled bismuth resistor forms a branch of a Wheatstone bridge across which a fixed voltage is applied whereby the output voltage of said Wheatstone bridge is proportional to said control signal voltage.

5. A voltage multiplier comprising a controlled bismuth resistor. a controlling bismuth resistor, an electromagnet. an electrical network having the controlled bismuth resistor as an inte ral part thereof. having input terminals for application of an external signal multiplicand voltage and having output terminals at which a voltage appears proportional to the resistance of said resistor and to the multiplicand voltage, said bismuth resistors being in the field of said electromagnet, first terminal means for application of -an independent arbitrary voltage, resistor means connected thereto and forming with the said controlling bismuth resistor a network including a junction terminal at which a comparison voltage appears responsive to said independent arbitrary voltage and the resistance of said controlling bismuth resistor, second terminal means for application of an external multiplier voltage, servo means for controlling the current in said electromagnet. differential input connections to said servo means from said second terminal means and said junction terminal to control the magnetic flux density in the field of electromagnet by said servo means in response to relationship between comparison and multiplier voltages, whereby the resistance of the said controlling bismuth resistor is controlled in synchronism with said external multiplier voltage and the resistance of the controlled bismuth resistor is controlled in synchronism with said controlling bismuth resistor, thereby multiplying said external signal multiplier voltage by said external signal multiplicand voltage.

6. A voltage divider comprising a controlled resistor, a controlling resistor both having the property of varying in resistance with magnetic field, an electromagnet, an electrical network having said controlled resistor as an integral part having input terminals for application of an external signal dividend voltage. and having output terminals at which a voltage appears proportional to resistance of said controlled resistor and to the dividend voltage, said resistors being in the field of said electromagnet, input terminal means for application of an external signal divisor voltage. network resistance means connected to said input terminal means. said controlling resistor also being connected to said input terminal means and form ing with said resistance means a network including a junction terminal at which a comparison voltage appears in response to said divisor voltage, servo means for controlling the current in said electromagnet having an input connection from said junction terminal for controlling the magnetic flux density in response to the external signal divisor voltage whereby the resistance of said controlling resistor is controlled in synchronism with, and in inverse proportion to, said external signal divisor voltage and the resistance of said controlled resistor is controlled in synchronism with said controlling resistor, thereby dividing said external dividend voltage by said external divisor voltage.

7. A device for multiplying a first arbitrary voltage by a second arbitrary voltage comprising a first and a second Wheatstone bridge; four precision bismuth resistors, two of said precision bismuth resistors being contained in each of said Wheatstone bridges; an electromagnet, one of said bismuth resistors in each of said Wheatstone bridges being positioned within the magnetic field of said electromagnet; a field current controller for controlling the current in the coil of said electromagnet; a direct coupled amplifier for operating said field current controller; a resistance network for applying a voltage to said direct coupled amplifier, said resistance network being adapted to compare said first arbitrary voltage with the voltage generated at the output of said first Wheatstone bridge when a constant voltage is applied to the input of said first Wheatstone bridge, the difference in the voltage between said first arbitrary voltage and said output voltage from said first Wheatstone bridge being applied to the input of said direct coupled amplifier, said amplifier operating said field controller which in turn changes the flux density of said electromagnet causing the resistance of said bismuth resistors in said magnetic field to change value, thus causing a voltage proportional to said first arbitrary voltage to appear at the output of each of said Wheatstone bridges, thereby superimposing said first arbitrary voltage upon said second arbitrary voltage which is applied to the input of said second Wheatstone bridge whereby the output of said second Wheatstone bridge is the product of the two said arbitrary voltages.

8. A device for dividing a first arbitrary voltage by a second arbitrary voltage, comprising a first and a second Wheatstone bridge; four precision bismuth resistors, two of said bismuth resistors being in each of said Wheatstone bridges; an electromagnet, one of said bismuth resistors in each of said Wheatstone bridges being within the magnetic field of said electromagnet; a field current controller for controlling the current through the coil of said electromagnet; a direct coupled amplifier for operating said field current controller; a resistance network for applying a voltage to said direct coupled amplifier, said resistance network being adapted to compare said first arbitrary voltage with the voltage generated at the output of said first Wheatstone bridge, the difference in voltage between said first arbitrary voltage and said output voltage from said first Wheatstone bridge when said second arbitrary voltage is applied to the input of said first Wheatstone bridge being applied to the input of said direct coupled amplifier, said amplifier causing the flux density of said electromagnet to change by means of said field current controller, thus causing said magnetic field and the resistance of bismuth resistors to change value in accordance with said first arbitrary voltage divided by said second arbitrary voltage whereby the output voltage of said second Wheatstone bridge will be proportional to said first arbitrary voltage divided by said second arbitrary voltage when a constant voltage is applied to the input of said second Wheatstone bridge.

9. A device for multiplying a first arbitrary voltage by a secondary arbitrary voltage, comprising a first Wheat stone bridge and a second Wheatstone bridge; four precision bismuth resistors, two of said precision resistors being in each of said Wheatstone bridges; an electromagnet, one of said bismuth resistors in each of said Wheatstone bridges being positioned within the magnetic field of said electromagnet; servo means adapted to compare said first arbitrary voltage with the voltage output from the said first Wheatstone bridge and to change said magnetic field so that the output voltage from each of said Wheatstone bridges has a component proportional to said first arbitrary voltage, the said component in the said second Wheatstone bridge being thereby multiplied by said second arbitrary voltage appliedto the input of said second Wheatstone bridge whereby said first arbitrary voltage is multiplied by said second arbitrary voltage with high input impedance, high fidelity, zero phase shift, and zero voltage output for zero voltage input.

10. A device for dividing a first arbitrary voltage by a second arbitrary voltage comprising a first Wheatstone bridge and ,a second Wheatstone bridge, four precision bismuth resistors, two of said precision bismuth resistors being in each of said Wheatstone bridges, an electromagnet, one of said bismuth resistors in each of said Wheatstone bridges being positioned within the magnetic field of said electromagnet, servo means adapted to compare said first arbitrary voltage with the output voltage from the said first Wheatstone bridge .when said second arbitrary voltage is applied to the input of said first Wheatstone bridge and to change said magnetic field so that the output voltage from said Wheatstone bridge has a component proportional to the said first arbitrary voltage, the output voltage from said second Wheatstone bridge having a component proportional to the said first arbitrary voltage divided by the said second arbitrary voltage when a constant voltage is applied to the input of said second Wheatstone bridge whereby said first arbitrary voltage is divided by said second arbitary voltage with high input impedance, high fidelity, zero phase shift,

and zero voltage output for zero voltage input.

11. A device for dividing a first arbitrary voltage by a second arbitrary voltage, comprising a first Wheatstone bridge and a second Wheatstone bridge; four precision bismuth resistors, two of said precision resistors being in each of said Wheatstone bridges; an electromagnet, one of said bismuth resistors in each of said Wheatstone bridges being positioned within the magnetic field of said electromagnet; servo means to. compare the voltage output from said first Wheatstone bridge with a constant voltage when said second arbitrary voltage is applied to the input of said first Wheatstone bridge and to change said magnetic field in a manner so that the output voltage from said first Wheatstone bridge will remain proportional to said constant voltage while the output voltage from said second Wheatstone bridge has a component proportional to the reciprocal of said second arbitrary voltage when said first arbitrary voltage is applied to the input of said second Wheatstone bridge whereby said first arbitrary voltage is divided by said second arbitrary voltage with high input impedance, high fidelity, zero phase shift, and zero voltage output for zero voltage inut. p 12. A device for dividing a first arbitrary voltage by a second arbitrary voltage and multiplying the quotient voltage by a third arbitrary voltage, comprising a first Wheatstone bridge and a second Wheatstone bridge; four precision bismuth resistors, one of said bismuth resistors being in each of said Wheatstone bridges; an electromagnet, one of said bismuth resistors in each of said Wheatstone bridges being positioned within the magnetic field of said electromagnet; servo means adapted to compare said first arbitrary voltage with the voltage output from the said first Wheatstone bridge when said second arbitrary voltage is applied to the input of said first Wheatstone bridge and to change said magnetic field so that the output voltage from said first Wheatstone bridge has a component proportional to said first arbitrary voltage while the output voltage from said second Wheatstone bridge has a component proportional to said first arbitrary voltage divided by said second arbitrary voltage when said third arbitrary voltage is applied to the input of said second Wheatstone bridge whereby said first arbitrary voltage is divided by said second arbitrary voltage and the quotient voltage is then multiplied by said third arbitrary voltage with high input impedance, high fidelity, zero phase shift, and zero voltage output with zero voltage input.

13. In a device for multiplying a first'arbitrary voltage by a second arbitrary voltage; an electromagnet; at least two bismuth resistors; a first resistance network and a second resistance network similar to said first resistance network; said bismuth resistors being in the field of said electromagnet, the first of said bismuth resistors being a part of said first resistance network, the second of said bismuth resistors being a part of said second resistance network; servo means for controlling the current in said electromagnet; said first resistance network adapted to compare the voltage appearing by virtue of the change of the resistances of said first bismuth resistor with said first arbitrary voltage and to control the flux density of said electromagnet by said servo means causing the re-' sistances of said second bismuth resistor in said second resistance network to change in synchronism with the resistance of said first bismuth resistor in said first resistance network whereby said first arbitrary voltage applied to said first resistance network is instantaneously multiplied with negligible time delay by said second arbitrary voltage applied to the said second resistance network.

14. A modulator for modulating a first input voltage by a second input voltage, comprising a first input circuit and a second input circuit; .an electromagnet; an electromagnet control circuit, bismuth resistors within the field of said electromagnet, the first of said bismuth resistors being an integral part of said first input circuit, the second of said bismuth resistors being an integral part of said second input circuit; a high gain direct coupled amplifier; said first input circuit being adapted to compare said first input voltage with the voltage appearing by virtue of the change of resistance of said first bismuth resistor and to deliver the difierence between the said first input voltage and said voltage v.ppearing by virtue of the change of resistance of said first bismuth resistor to said direct coupled amplifier which in turn controls the current in said electromagnet in a direction to reduce said dilference voltage to zero, the second said input circuit being symmetrical with the first said input circuit so that voltages which are proportional to said first input voltage appear in said second input circuit by virtue of the change of resistance of said second bismuth resistor, said first input voltage being superimposed upon said second input voltage whereby said first input voltage is modulated by said second input voltage.

15. Means for multiplying a first varying voltage by a second varying voltage comprising a first bridge network including two bismuth resistors in series, a second bridge network including two bismuth resistors in series, an electromagnet for varying the resistance of only one of said bismuth resistors in each said network, and means for controlling the magnetic field of said electromagnet to cause the voltage between the junction of the bismuth resistors in said second network and the junction of the other resistors therein to be proportional to said first varying voltage whereby the voltage between the junction of the two bismuth resistors of said first network and the junction of the other two resistors therein is proportional to the product of said first varying voltage and said second varying voltage if said second varying voltage is applied to said first network of hismuth resistors in series.

16. Means for multiplying a first varying voltage by a second varying voltage comprising a first bridge network including a bismuth resistor in one of its branches, a second bridge network including a bismuth resistor in one of its branches, an electromagnet for varying the resistance of said bismuth resistors in each of said networks, and means for controlling the magnetic field of said electromagnet to cause the voltage across said bridges between the junction of one end of each bismuth resistor and an adjacent resistor and the junction of the other resistors therein to be proportional to said first varying voltage whereby the voltage between the junction of 11 12 the bismuth resistor and its adjacent resistor in said first References Cited in the file of this patent network and the junction of the other two resistors in UNITED STATES PATENTS said first network is proportional to the product of said 543,843 Biggar Aug. 6 1895 first varying voltage and said second varying voltage when said second varying voltage is applied to the first 5 gg fig scherbagskoy Sept 1938 network of said bismuth resistors in series. Mccou my 1951 

1. MEANS FOR CAUSING THE RESISTANCE OF A BISMUTH RESISTOR TO VARY ACCURATELY IN RESPONSE TO VARIATION IN A FUNCTION OF AT LEAST ONE INDEPENDENT VARIABLE VOLTAGE COMPRISING A CONTROLLED BISMUTH RESISTOR HAVING THE PROPERTY OF VARYING IN RESISTANCE WITH MAGNETIC FIELD, A CONTROLLING BISMUTH RESISTOR HAVING THE SAME PROPERTY, FIRST AND SECOND TERMINAL MEANS FOR APPLICATION OF FIRST AND SECOND INDEPENDENT ARBITARY VOLTAGES, ONE OF WHICH CONSTITUTES A CONTROL SIGNAL, RESISTANCE MEANS FORMING WITH SAID CONTROLLING BISMUTH RESISTOR A RESISTANCE NETWORK INCLUDING JUNCTION TERMINAL AT WHICH A COMPARISON VOLTAGE IS ADAPTED TO APPEAR, THE FIRST OF SAID TERMINAL MEANS BEING CONNECTED TO SAID RESISTANCE NETWORK FOR ENERGIZING IT TO PRODUCE A COMPARISON VOLTAGE AT SAID JUNCTION TERMINAL, AN ELECTROMAGNET, SEVO MEANS CONNECTED THERETO AND HAVING INPUT TERMINALS TO WHICH SAID SECOND TERMINAL MEANS AND SAID NETWORK JUNCTION TERMINALS ARE DIFFERENTLY CONNECTED FOR RENDERING THE SERVO MEANS RESPONSIVE TO RELATIONSHIP OF VOLTAGES AT SAID SECOND TERMINAL MEANS AND THE SAID JUNCTION TERMINAL, SAID BISMUTH RESISTORS BEING WITHIN THE MAGNETIC FIELD OF SAID ELECTROMAGNET, SAID SERVO MEANS BEING CONNECTED TO CONTROL THE FIELD STRENGTH OF SAID ELECTROMAGNET IN RESPONSE TO THE DEVIATION FROM A PREDETERMINED RELATIONSHIP BETWEEN VOLTAGES AS SAID SECOND TERMINAL MEANS AND SAID JUNCTION TERMINAL SO THAT SAID DEVIATION APPROACHES ZERO, WHEREBY THE RESISTANCE OF SAID CONTROLLED BISMUTH RESISTOR IS CAUSED TO VARY IN PROPORTION TO THE RESISTANCE OF SAID CONTROLLING RESISTOR. 